Rigid-bodied robots generally excel at specific tasks in structured environments, but lack the versatility and adaptability required to interact with and locomote within the natural world. To achieve maximum versatility in soft robot design, we present robotic skins that can wrap around arbitrary soft bodies to induce desired motions and deformations. Robotic skins integrate actuation and sensing into a single conformable material, and may be leveraged to create a multitude of controllable soft robots with different functions or gaits to accommodate the demands of different environments. We show that attaching the same robotic skin to a soft body in different ways, or to different soft bodies, leads to unique motions. Further, we show that combining multiple robotic skins enables complex motions and functions. We demonstrate several instances of this versatile soft robot design paradigm by creating a continuum robot, multiple locomotion robots, and a grasping end-effector, all using the same 2D robotic skins reconfigured on the surface of various 3D soft, inanimate bodies.